Answer :
To solve the inequality [tex]\(\sqrt{x} > 9\)[/tex], we need to determine the values of [tex]\(x\)[/tex] that satisfy this condition.
1. Remove the square root by squaring both sides: Starting with [tex]\(\sqrt{x} > 9\)[/tex], we square both sides to get rid of the square root:
[tex]\[
x > 9^2
\][/tex]
2. Calculate [tex]\(9^2\)[/tex]: Now we find the value of [tex]\(9^2\)[/tex], which is:
[tex]\[
9^2 = 81
\][/tex]
3. Determine the inequality: The inequality [tex]\(x > 81\)[/tex] tells us that [tex]\(x\)[/tex] should be greater than 81.
4. Check each option:
- Option A: 82, 83, 84
Each of these numbers (82, 83, and 84) is greater than 81. Therefore, this option satisfies the inequality.
- Option B: 3, 4, 5
All these numbers are much less than 81, so this option does not satisfy the inequality.
- Option C: 4, 5, 6
Similar to option B, these are also much less than 81, which means this option doesn't satisfy the inequality.
- Option D: 81, 82, 83
Here, 81 is equal to the threshold, which does not satisfy the strict inequality [tex]\(x > 81\)[/tex]. However, 82 and 83 are greater than 81, but since not all numbers in the list satisfy the condition, this option doesn't fully satisfy the inequality.
Therefore, the list that contains all numbers greater than 81 is Option A: 82, 83, 84.
1. Remove the square root by squaring both sides: Starting with [tex]\(\sqrt{x} > 9\)[/tex], we square both sides to get rid of the square root:
[tex]\[
x > 9^2
\][/tex]
2. Calculate [tex]\(9^2\)[/tex]: Now we find the value of [tex]\(9^2\)[/tex], which is:
[tex]\[
9^2 = 81
\][/tex]
3. Determine the inequality: The inequality [tex]\(x > 81\)[/tex] tells us that [tex]\(x\)[/tex] should be greater than 81.
4. Check each option:
- Option A: 82, 83, 84
Each of these numbers (82, 83, and 84) is greater than 81. Therefore, this option satisfies the inequality.
- Option B: 3, 4, 5
All these numbers are much less than 81, so this option does not satisfy the inequality.
- Option C: 4, 5, 6
Similar to option B, these are also much less than 81, which means this option doesn't satisfy the inequality.
- Option D: 81, 82, 83
Here, 81 is equal to the threshold, which does not satisfy the strict inequality [tex]\(x > 81\)[/tex]. However, 82 and 83 are greater than 81, but since not all numbers in the list satisfy the condition, this option doesn't fully satisfy the inequality.
Therefore, the list that contains all numbers greater than 81 is Option A: 82, 83, 84.
